Chambers joined Arsenal from Southampton in the summer of 2014 for a fee of £16m but, after an initial bright start, his career in north London seemed to stall, culminating in a season-long loan move to Middlesbrough last summer.
The 22-year-old's temporary spell at the Riverside did not pan out as he may have hoped - Boro were relegated to the Championship after just a single season in the Premier League - but Keown thinks the England Under-21 international could flourish in north London if Wenger keeps utilising a three-man defensive system, which garnered success towards the back-end of a rather disappointing season for Arsenal.
Everton were recently reported to be exploring the possibility of a £15m bid for Chambers if their move for Burnley defender Michael Keane does not come to pass. Everton manager Ronald Koeman is eager to bolster his defensive options ahead of next season but he could face competition from the likes of West Ham United and Newcastle United should he push for a move for the former Southampton starlet.
A move to Everton, West Ham or another club is a distinct possibility, but Keown does not think Chambers should give up hope on revitalising his Arsenal career just yet.
"If Arsenal play three centre halves that means there could be chances for him [Chambers]," Keown told Arseblog. "I think he looks very suited to that system. Arsene tends to keep faith in younger players, the issue might be if other clubs come in for him, does the player want to hang around if he can start somewhere else?
"He'll have watched the FA Cup success from afar and been a little envious, but we'll have to see what ambitions he has now. He seems a very well balanced guy. There was a little debate as to whether he was a right-back or a centre-half. In a back three, he might find that balance and Wenger might have a plan for him."
Chambers' chances of game-time at Arsenal next season may be limited due to the presence of Rob Holding, who impressed greatly during the dying embers of the last campaign. The 21-year-old cost a paltry £2m from Bolton Wanderers, an "exceptional piece of business", according to Keown.
"I've been really impressed," Keown said. "He's quietly understated and doesn't get ruffled by anything. He's very calm in possession and uses the ball well. He really benefits from being in a three.
"When you're a young central defender, it's nice to have that extra player around you and his positioning is already very good in that formation. When you consider [Manchester] City paid upwards of £50m for [John] Stones and Arsenal paid £2m for Holding, that's another exceptional piece of business from Arsene Wenger."